A simple random sample of 1000

A simple random sample of 1000 elements generates a sampleproportion p =0.68  

a. Provide the confidence interval for the population proportion(to 4 decimals). ,

(     , )

b. Provide the confidence interval for the population proportion(to 4 decimals). ,

( , )

Answer:

CONFIDENCE INTERVAL IS NOT GIVEN SO WE ASSUME FOR PART A-99% ANDFOR PARTB-90%

a)

Levelof Significance,   α = 1- 0.99= 0.01  Sample Size,   n =    1000            Sample Proportion ,    p̂ =    0.68

z -value =   “Zα/2 = 2.5758 FROM CRITICAL VALUE TABLE

Standard Error ,    SE = √[p̂(1-p̂)/n] =   0.01475

marginof error ,    E = Z*SE =    0.0380

Confidence Interval         Interval Lower Limit , =    p̂ – E =   0.6420Interval Upper Limit , =    p̂ + E =  0.7180

b)

Levelof Significance,   α =1- 0.90 = 0.1  Sample Size,   n =    1000            Sample Proportion ,    p̂ =    0.68z -value =   “Zα/2 =1.6449

Standard Error ,    SE = √[p̂(1-p̂)/n] =   0.01475          margin of error ,    E = Z*SE =    0.0243          Confidence Interval         Interval Lower Limit , =    p̂ – E =   0.6557Interval Upper Limit , =    p̂ + E =  0.7043


 
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